For questions on dice, a small throwable object with multiple resting positions, used for generating random numbers. This makes dice suitable as gambling devices for games like craps, or for use in non-gambling tabletop games.

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12 six-sided dice are thrown, what is the probability of getting each number at least once? [duplicate]

I got a bit confused and couldn't find the correct answer to check mine. This was the closest I could get: $\frac{6^6 \frac{12!}{6!6!}}{6^{12}}=\frac{924}{6^6}=0,0198$ where you have $12 ...
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1answer
36 views

Probability to obtain more than X with 3 dice.

This is a dice problem 1) I want to calculate the probability to have more than X throwing 3 dice of 6 faces. X = addition of the result of the 3 dice. 2) This is the first step but if you can also ...
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1answer
45 views

Probability Mass Function of infinitely re-rolled dice

I play a game called Shadowrun. It is a role-playing game that uses a dice pool mechanic. A player has a dice pool of $x$ six-sided, unbiased dice. Every 5 or 6 counts as a success. The more ...
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2answers
49 views

The probability of rolling 4 dice and getting a 6.

The probability of rolling 2 dice and getting a 6 on either one of the die or both is : 11/36 or about 0.305. Also I calculate the probability of rolling 4 dice and getting a 6 on either one, two, ...
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2answers
26 views

Dice role: What is the probability to observe 2 times 1 and 2 times 5 with the outcome of a fifth die role being unknown?

I tried to solve the following exercise: Given a dice with $P(X=2) = P(X=4) = P(X=5) = \frac{2}{15}$ and $P(X=1) = P(X=6) = P(X=3) = \frac{2}{10}$. What is the probability to observe 2 times 1 and 2 ...
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1answer
15 views

Probability of rolling a five and a prime pair of six sided dice

This is a silly question, but I can't quite put my finger on where my reasoning is wrong. Given a pair of 6 sided dice, what is the probability of rolling a 5 and a prime? My answer: 6/36 Correct ...
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0answers
59 views

Generalization of classic 3 roll die game to $n$ rolls

I am trying to generalize the following well-known 3 roll die problem: "We roll a single die no more than 3 times. We can stop immediately after the first roll, immediately after the second roll, or ...
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69 views

Progressive Dice Game

You have a fair, regular 6-sided dice. The game is played for $n$ turns. Each turn you make a roll and gain that many points the rolled side is showing, then do one of the following: ...
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1answer
22 views

Any way to calculate chances of getting “n” hits when rolling “x” die (hit is when I roll more than “y”)?

First, let me preface - I saw similar questions already, but to be honest, I didn't understand the answers, or couldn't understand how to convert the answer for given question to my problem. My ...
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0answers
20 views

Probability of the n-th dice matching in 2 groups of sorted random numbers

Say we have 2 groups of 6 6-sided dice. Each group of dice is rolled and then sorted so we have 2 groups of sorted numbers. What is the probability of each die in the group matching the corresponding ...
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1answer
41 views

Two regular dice are rolled. Given that one of them is a $6$, what is the probability that the other is also a $6$?

I'm having trouble with the following question for and I have an exam in two days: Two regular dice are rolled. Given that one of them is a $6$, what is the probability that the other is also a ...
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2answers
69 views

Proof: Probability of a pair when rolling 7 dice is 1.

I know that the probability should be over or exactly 1 since out 6 possible values the 7th dice will always be a duplicate. My calculations are wrong though: $\frac{{7\choose2} 5! 6*1}{6^7}$ ...
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2answers
46 views

Probability of disjoint dice results

You have $n = n_A + n_B$ $k$-sided dice. The $n_A$ dice are thrown and a set of the resulting values, call it $S_A$, is built; likewise for the $n_B$ dice, calling the resulting set $S_B$. What is ...
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1answer
37 views

What is the probability that the sum of two dice rolls is a multiple of $3$?

What is the probability that the sum of $2$ dice rolls is a multiple of $3$? What about for $3$ dice rolls? For $n$ dice rolls? So I have the first part of this solution worked out by writing out all ...
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1answer
55 views

Optimal bet according to the probability of win

Suppose the following game: You start with $5000; You will roll a dice 100 times; You have to choose a percentage of your accumulated money to bet all the 100 times. You will choose it only once and ...
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0answers
51 views

Dice throwing probability : at least one success

What would be the function for calculating the probability of at least one success of $n$ $10$-sided dice thrown, if success is $9$ or $10$, but $1$ is counted as negative success (or failure). In ...
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6answers
386 views

Die that never rolls the same number consecutively

Suppose we have a "magic" die $[1-6]$ that never rolls the same number consecutively. That means you will never find the same number repeated in a row. Now let's suppose that we roll this die $1000$ ...
4
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1answer
51 views

Special dice generating non-decreasing sequence

Suppose that, when rolled for the first time, a special 6-sided dice shows $1,\ldots, 6$ with probability $\frac{1}{6}$ each, and then, upon rerolling, shows with equal probability a number greater or ...
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1answer
38 views

Calculating probability that 5 dice rolls will produce an average of 3.5

We are carrying out a dice game which involves 5 people rolling dice and passing buttons equal to the number rolled . We have to work out the probability that we will get an average of 3 .5 items ...
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2answers
56 views

Dice probability, Heaven or Hell [closed]

You're at the gate of Heaven and St. Peter asks you to play Dice with him. If you roll a 5 or 6, he'll let you into Heaven. However, if you roll a 2,3 or 4, you'll be sent to hell. If you roll a 1, he ...
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2answers
37 views

Find dependent event when two dice are thrown simultaneously.

Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_1$ is the event that die $A$ shows up four, $E_2$ is the event that die $B$ shows up two and $E_3$ is the event that the sum of ...
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0answers
35 views

Can someone help me balance this game (probability question) [closed]

A team of 9 vs a team of 1. Each round each of "the 9" roll a die to "attack" and "the 1" rolls 9 dice to "defend", the nine dice are preassigned to attackers before the roll, "the 1" cannot choose ...
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1answer
32 views

Given three six-sided dice, what is the probability that the value of the third will be greater than the sum of those of the first two?

A die is rolled three times, or three dice are rolled. What is the probability that the third die values greater than the sum of the first two? (assuming six-sided dice, but I would be interested in ...
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1answer
29 views

Creating $Y \sim U[1, \dots, 6] + U[1, \dots, 6]$ as a function of $X_1, X_2, X_3 \sim U[1, \dots, 6]$

The Three Indistinguishable Dice Puzzle from standupmaths The problem therein can be summarized as follows: You have three dice rolls. Each die is indistinguishable from the others. However, using ...
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3answers
533 views

You cast a pair of dice. If you get a 6 and an 8 before 7 comes up twice, you win. What is the probability of winning?

You cast a pair of dice. If you get a 6 and an 8 before 7 comes up twice, you win. What is the probability of winning? What I tried was \begin{align*} P(X=6) & = \frac{5}{36}\\ P(X=8) & = ...
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4answers
1k views

Rolling a die until two rolls sum to seven

Here's the question: You have a standard six-sided die and you roll it repeatedly, writing down the numbers that come up, and you win when two of your rolled numbers add up to $7$. (You will ...
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2answers
42 views

What is the probability of these questions?

What is the probability of throwing $2$ dice, and the first one is a $6$? (Given that one of them is a 6.) My solution says that it's $\frac{6}{11}$, but I have no clue why. The other one is: What ...
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1answer
671 views

How to use N indistinguishable dice to simulate 1 roll of N-1 dice? [closed]

If I use 3 indistinguishable dice to simulate 1 roll of 1 die. I can use this formula "(SUM % 6) + 1". There SUM is the total amount of the three indistinguishable dice added together, 6 is the max ...
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3answers
1k views

Probability of three dice falling in the same quadrant of a box

This is surely really basic for most people here but it's tripping me up. You get a box and draw lines to split it up into 4 parts. I got asked what the probability was that when rolling three ...
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0answers
50 views

Roll two fair dice, what is the expected value of rolls such that the sum of the two faces is the multiple of 6.

I was thinking that there were 2 cases: (1) $\\$ $X_{1}+X_{2}=6$, and the probability would be $\dfrac{5}{36}$. (2) $\\$ $X_{1}=X_{2}=6$, and the probability would be $\dfrac{1}{36}$. I am now ...
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1answer
51 views

Probability of being able to make a given number with two out of xd6

I'm an amateur games designer, and am working on a mechanic which involves rolling on a table with numbers running from 2-12 - the full range of possibilities from adding together two six-sided dice. ...
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2answers
38 views

Rolling dice against each other?

After doing some research, I found that the probability of rolling an n-sided die against another, equivalent die and landing a higher number on the first rolled dice to be ((n−1)/2)/n, where n is the ...
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2answers
28 views

Probability of Rolling a $1$ on an $n$-Die in $r$ Attempts

I roll an $n$ sided die, numbered $1 \to n$. If I roll a $1$, I walk away; otherwise, I roll the die again. This process could repeat indefinitely. What is the probability, $P(n,r)$, that I will roll ...
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0answers
28 views

7th Sea 2e: Grouping dice results into sets of 10 vs doing the same with Tarot cards.

Note: While an interesting problem on its own, it also struck me as an excellent example of how marvelous the human brain is, as it is able to almost effortlessly negotiate a task that (at least to ...
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4answers
1k views

Probability of obtaining a heads on the coin before a 1 or 2 on the die?

I came across this question recently and can't seem to find the correct approach. Any help would be appreciated! An experiment consists of first tossing an unbiased coin and then rolling a fair ...
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1answer
60 views

Probability of rolling dice twice

Did I calculate the correct probability for these simple scenarios: 1: What is the probability of rolling 3 and 4 with two dice in two rolls? If you roll either 3 or 4 in the first roll, you put ...
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1answer
55 views

If you roll four dice what is the probability of getting at least two sixes?

First of all, I know there are a lot of these and similar questions already online but I am trying to solve this on my own and I need you to tell me what I am doing wrong. So, in class we solved ...
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1answer
24 views

Probability of $3$ doubles when two dice roled $4$ times

I thought that when rolling two dices to get only pairs is for a single roll $\frac{1}{6}$ for two $\left(\frac{1}{6}\right)^2$, and for three $\left(\frac{1}{6}\right)^3$. But since I have 4 rolls ...
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0answers
69 views

How to statistically beat this dice game?

There is a dice game on this site where you can bet a video game's currency in games. I was wondering if any of the more statistically minded could come up with a way of beating the system? The game's ...
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1answer
81 views

Dice probability with limited reroll

What is the probability of getting 2 successes when 3 dice are rolled once, and then one die is optionally rerolled? $$ n = \text{Number of dice} = 3 $$ $$ p_s = \text{Single die success probability ...
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1answer
60 views

Rolling a biased dice, Multinomial probability

What is the easiest way to answer this question. Lets say you had a biased 6-sided die P(rolling '1') = P(rolling '3') = 0.1 P(rolling '2') = P(rolling '4') = P(rolling '6') = 0.25 P(rolling '5') ...
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2answers
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1answer
42 views

How many rolls of two dice are needed so that the probability of rolling a double six within this number of rolls is at least $50\%$?

My approach: How many rolls of two dice are needed so that the probability of rolling a double six within this number of rolls is at least $50\%$? Let $X$ be the number of required rolls. ...
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2answers
31 views

Rolling the results at the same time as the check

I was in a roll playing game last night. In combat we throw 3 six sided dice when we attack and roll some amount of dice if we hit our target by rolling high enough on the attack (for example the dice ...
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0answers
39 views

Most Probable Sum for Dice Rolls

Hey so I discovered this formula for finding out the most probabble result when rolling a certain number of f-sided dice. Could you check it and tell me why it is so? ...
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1answer
21 views

Probabilities of reoccuring draws in a stack of cards

Let's say I have a stack of $12$ cards where only one card in the set is a golden card. The cards are displayed face down on the table in a $3\times4$ pattern and I can choose one card at the time. As ...
14
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2answers
239 views

Rolling $n$ $k$-sided dice and discarding the lowest $m$ of them.

In this question I will use the notation $\Bbb{E}(n,k,m)$ to refer to the expected average of rolling $n$ $k$-sided dice and discarding the lowest $m$ of them. The most trivial response happens ...
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2answers
45 views

Rolling four dice and the difference between predictions

Four standard dice are rolled. What are the chances of: 1.) Rolling three sixes and one five? 2.) Two sixes and two fives? 3.) Exactly one six? 4.) Four different numbers? Here is my thought ...
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4answers
896 views

On the probability of getting the same number for three dice

I found the probability of having the same number when throwing 3 dice to be $1\times\left(\frac16\right)^2$. In addition, I don't understand how do people get the equation ...
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1answer
41 views

Comparative Dice Statistics

I am part of a role playing game where we roll dice to set our statistics. Our current system is to roll 4d6, reroll the lowest of the 4, then keep the highest 3 out of the original 3 and the new one ...